Covey (3-1) allowed 10 hits - all singles - and walked none. The 26-year-old right-hander improved to 3-0 with a 1.53 ERA in five starts since he was recalled from Triple-A Charlotte last month.

The White Sox got Covey from Oakland in the 2016 Rule 5 draft. He went 0-7 with a 7.71 ERA in 18 games, 12 starts, last season, but he has looked like a different pitcher since returning to the majors.

"I'm just super comfortable, with my mechanics, with my pitches," he said. "I'm throwing offspeed for strikes, I'm throwing my curveball for strikes. It's just all about comfort for me right now."

Covey got a warm ovation from the crowd of 19,390 when he departed after the first two batters reached in the eighth. Edwin Encarnacion hit a one-out RBI single and Yonder Alonso doubled home another run before Jace Fry struck out Melky Cabrera and Jason Kipnis, preserving Chicago's 3-2 lead.

Joakim Soria allowed two more hits in the ninth before finishing for his 10th save in 12 chances. Michael Brantley bounced into a game-ending double play with runners on first and second.

Cleveland wasted another impressive start for Bauer in its second straight loss after a stretch of five wins in six games. Brantley had three hits, but the AL Central leaders went 2 for 13 with runners in scoring position and left nine runners on base.

Bauer (5-5) struck out 12 in 7 2/3 innings while becoming the third pitcher in franchise history to record at least 10 Ks in four consecutive starts, joining teammate Corey Kluber and Hall of Famer Bob Feller.

"Missing a lot of bats, limited contact, keeping the ball in the yard, not walking many people. It was a great outing," Bauer said.

Bauer matched Covey zero for zero until the White Sox scratched across two in the fifth. Tim Anderson walked, stole second and went to third on a throwing error by catcher Roberto Perez before Charlie Tilson tripled into the corner in right . Tilson then scampered home on Trayce Thompson's perfectly placed suicide squeeze.

Kevan Smith added an RBI single in the sixth as Chicago won for the third time in four games.

HELPING OUT

White Sox first baseman Jose Abreu helped Covey by turning a pair of slick double plays. He also doubled and scored on Smith's single.

TRAINER'S ROOM

Indians: LHP Andrew Miller (left knee inflammation) threw another bullpen session and could start facing hitters during Cleveland's upcoming nine-game homestand. ... Francona said the plan is to activate OF Brandon Guyer (strained neck) on Thursday. ... C Roberto Perez returned to the lineup for the first time since he was hit by a pitch on the right wrist against Detroit on Sunday. ... OF Bradley Zimmer, who was sent down to Triple-A Columbus on June 5, hurt his right shoulder in a drill Monday. He is expected to rest for five days.

White Sox: RHP Nate Jones was placed on the 10-day disabled list with a muscle strain in his forearm. The veteran reliever had an MRI, and Renteria said the injury is "very mild." RHP Juan Minaya was recalled from Triple-A Charlotte to take Jones' place on the roster. ... OF Avisail Garcia (strained right hamstring) went 0 for 3 with two strikeouts in his second rehab game with Charlotte.

UP NEXT

Indians right-hander Mike Clevinger and White Sox left-hander Carlos Rodon start the series finale Thursday afternoon. Clevinger (4-2, 3.31 ERA) pitched 6 2/3 innings of one-run ball in a 7-3 victory over Chicago on May 29. Rodon (0-1, 3.60 ERA) is making his second start after missing the beginning of the season while he worked his way back from shoulder surgery last September.